The counting process and summation of a random number of random variables

Abstract

Abstract. The behavior of the tail of the sum of a random number of random variablesEstimates of the convergence of F (x) to the limit function are constructed in terms of renewal theory. The estimates are based on the variance Var ν(t) of the counting process ν(t) = min n :A survey of bounds for Var ν(t) is given for different sequences {ξ i }, in particular, for the case where the terms of the sequence {ξ i } are not identically distributed.